London's calling: One in three 22- to 30-year-olds leave their hometowns to end up with Oyster cards and Boris Johnson as their mayor. Photograph: Bloomberg via Getty Images

Boris Johnson got into hot water recently with his claim that London, not Liverpool, was responsible for the success of the Beatles. The Fab Four might have been born on Merseyside, the capital mayor's said, but London turned them into the biggest band of all time.

While that was the cue for Liverpudlian indignation at what was seen as cultural piracy, a new report out on Monday suggests the arrival of the Beatles at Abbey Road Studios in 1962 to cut Love Me Do was an early example of a now dominant trend.

Talented young people are leaving provincial cities in their 20s, making a success of their lives in London and never go back. London is where the work is: the capital was responsible for four out of every five jobs created in the private sector between 2010 and 2012.

The brain drain meant that every major city outside the south-east is losing young people to London. One in three 22-30 year olds leaving their hometowns end up with Oyster cards and Boris as their mayor.

They don't always stay in the capital. Alexandra Jones, chief executive of the thinktank Centre for Cities, says that in their 30s many of those attracted by the bright lights of the capital tire of London and move out when they want to start families.

But they follow the example of John Lennon, who bought a mansion in Ascot, Paul McCartney with his farmhouse in Sussex and George Harrison with his spread in Oxfordshire in plumping for the home counties over returning to their roots.

The Fab Four might have been born on Merseyside, Boris Johnson said, but London turned them into the biggest band of all time. Photograph: Alamy

Jones says this pattern explains why it is misleading to see London, as some do, as the equivalent of a city state, cut off from the rest of the country. It is more accurate to say Britain is divided between London and its south-east hinterland and the rest. London does not end at the M25 but extends up the M11 towards Cambridge, down the Thameslink line to Brighton and along the M4 corridor where many high-tech companies are based.

If the giant sucking sound of London draining talent from the rest of the UK is one highlight of the Centre for Cities report, the other is the capital's ability to create jobs. Young people come to London because that's where the work is.

In the three years from 2010 to 2012 –a period marked by weak growth and austerity – London accounted for 10 times as many private sector jobs as any other city and also bucked the national trend by seeing an increase in public sector employment.

Highlighting the need for better infrastructure, investment in skills and reforms to planning, the report noted that Bradford, Sheffield, Bristol, Southampton, Blackpool and Glasgow saw employment shrink in both private and public sectors.

Jones, said: "Cities Outlook 2014 shows that the gap between London and other UK cities is widening and we are failing to make the most of cities' economic potential."

She added that Britain was one of the world's most centralised countries. In Germany, she said, the government was in Berlin, the financial centre was Frankfurt and there were cultural hubs in Hamburg and Munich. In the UK, London had it all.

What's more, the Treasury kept a much tighter hold of the purse strings than finance ministries in other rich nations. Local government raised 17% of its income from local taxation in the UK, compared to an average of 55% for other members of the Organisation for Economic Cooperation and Development, a club of more than 30 rich countries.

Jones said the government should build on City Deals – an attempt to allow some of the UK's bigger cities more control over their economic destinies – and "devolve more funding and powers to UK cities" in order to ensure a "sustainable, job-rich recovery across the country."

Nick Clegg, the deputy prime minister said the report showed the value of "tailoring policies to the distinctive needs of different cities". He added the government had been working to free cities from Whitehall control.

Hilary Benn, the shadow communities and local government secretary, said the report drew attention to "persistent and widening inequalities between different parts of the country", and agreed with Clegg and Jones that more power, resources and responsibility needed to devolved.

Centre for Cities said regeneration strategies in some of the UK's bigger cities were starting to pay off. Birmingham and Manchester saw an increase in both private and public sector jobs between 2010 and 2012, while in Liverpool the loss of public sector jobs was more than compensated for by the creation of private sector employment.